<p>Multi-fidelity (MF) surrogate models have become a promising way in simulation-based optimizations, particularly when high-fidelity simulations are computationally expensive. Adaptive optimization approach has shown great potential in improving the efficiency of multi-fidelity surrogate-based optimizations. Current adaptive optimization approaches, however, primarily focus on deterministic scenarios. It is also essential to consider the inevitable uncertainties in practical engineering optimization. This work proposes a novel adaptive multi-fidelity surrogate-based robust optimization approach that considers the combined effect of multiple uncertainty sources. The uncertainties from design variables, surrogate models, and model parameters are considered during the adaptive robust optimization process. Specifically, a systematic robust sampling strategy is derived for adaptively selecting the new sampling locations. The proposed approach is verified with analytical examples and an engineering application to a metamaterial vibration isolator design. Results show that the proposed adaptive robust optimization approach achieves more reliable and efficient optimization outcomes compared with the existing approaches.</p>